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Abstract
A chemostat with two organisms competing for a single growth-limiting nutrient
controlled by feedback-mediated dilution rate is analyzed. A specific
feedback
function is constructed which yields circular and elliptical periodic
orbits for the limiting system. A theorem on the stabilization of periodic
orbits in conservative systems is developed and for a given elliptical orbit,
the result is used to modify the chemostat so that the chosen orbit is
asymptotically stable. Finally, the feedback function is
modified so that finitely many nested periodic orbits of alternating
stability exist.
Mathematics Subject Classification: 92D25, 92D37, 92D45.
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